In traditional quantum measurement theory [1]}, the unitary process is considered as a process to entangle the measured system with the measuring apparatus before the projection process. The projection process gives definite final outcome. P2 essentially assumes the unitary process itself can have measurement result and can be assigned a (one-time) probability. [2]} has already pointed out that such assumption leads to a contradiction. But there is another problem with P2. [3]} assumes that the joint probability \(p(f_1,f_2)\)  is derived through the standard probability axiom \(p(f_1,f_2)=p(f_2|f_1)p(f_1)\) , but does not give details on how the conditional probability is calculated in quantum theory. It is not clear how the unitary formulation presented in [3]} can be applied to derive the conditional probability \(p(f_2|f_1)\) , because P2 assumes there is no “collapse" after the first measurement. It is not a problem to compute the one-time probability \(p(f_1)\)  and \(p(f_2)\) . But in order to be able to calculate a two-time probability such as \(p(f_2|f_1)\) , one will have to apply the state update rule after the first measurement at time \(t_1\) , as shown in (REF ) for the two-time conditional probability.
